Dmitriyev gave no time frame for the plane's delivery to Lebanon.
The export price tag on the Soviet-designed MiG-29, still seen as one of Russia's best war planes, is about $30m, industry experts say.
"We view the Lebanese army as a basic guarantor of political stability in the country and are ready to supply it with arms," Dmitriyev was quoted by Russian news agency Interfax as saying.
He also said Moscow was in talks with Beirut over the purchase of military hardware and training for its armed forces.
"We are now working jointly with our Lebanese colleagues on purchases of Russian armoured equipment, artillery and other military equipment for ground forces," he said.